Continuity

When Mike and Sulley are first shown their room at the fraternity house, the light switch is under the top bunk bed. In subsequent shots it has moved closer to the door and is no longer directly under the bed.

Plot holes

In the opening scene, when Mrs. Graves is counting students, she counts to 19 and then notices that Mike is missing, which means that there are 20 students in the class. If this were the case, he wouldn't have to pair up with the teacher.

According to Monsters, Inc, Mike and Sulley have known each other since 4th Grade because Sulley jokes with Mike about his face being seen on "Monstropolis's Most Wanted" and Mike responds with "You've been jealous of my good looks since the fourth grade, pal." However, according to this movie, they did not meet or become friends until they went to Monsters University together.